Mean absolute error (TheAlgorithms#10927)

* added mean absolute error to loss_functions.py

* added doctest to mean absolute error to loss_functions.py

* fixed long line in loss_functions.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* fixed error in MAE

* Update machine_learning/loss_functions.py

Co-authored-by: Tianyi Zheng <[email protected]>

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Tianyi Zheng <[email protected]>

machine_learning/loss_functions.py

@@ -261,6 +261,43 @@ def mean_squared_error(y_true: np.ndarray, y_pred: np.ndarray) -> float:
     return np.mean(squared_errors)
 
 
+def mean_absolute_error(y_true: np.ndarray, y_pred: np.ndarray) -> float:
+    """
+    Calculates the Mean Absolute Error (MAE) between ground truth (observed)
+        and predicted values.
+
+    MAE measures the absolute difference between true values and predicted values.
+
+    Equation:
+    MAE = (1/n) * Σ(abs(y_true - y_pred))
+
+    Reference: https://en.wikipedia.org/wiki/Mean_absolute_error
+
+    Parameters:
+    - y_true: The true values (ground truth)
+    - y_pred: The predicted values
+
+    >>> true_values = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
+    >>> predicted_values = np.array([0.8, 2.1, 2.9, 4.2, 5.2])
+    >>> np.isclose(mean_absolute_error(true_values, predicted_values), 0.16)
+    True
+    >>> true_values = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
+    >>> predicted_values = np.array([0.8, 2.1, 2.9, 4.2, 5.2])
+    >>> np.isclose(mean_absolute_error(true_values, predicted_values), 2.16)
+    False
+    >>> true_labels = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
+    >>> predicted_probs = np.array([0.3, 0.8, 0.9, 5.2])
+    >>> mean_absolute_error(true_labels, predicted_probs)
+    Traceback (most recent call last):
+    ...
+    ValueError: Input arrays must have the same length.
+    """
+    if len(y_true) != len(y_pred):
+        raise ValueError("Input arrays must have the same length.")
+
+    return np.mean(abs(y_true - y_pred))
+
+
 def mean_squared_logarithmic_error(y_true: np.ndarray, y_pred: np.ndarray) -> float:
     """
     Calculate the mean squared logarithmic error (MSLE) between ground truth and